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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Construction of convex sets in negatively curved manifolds
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by Albert Borbély
Proc. Amer. Math. Soc. 118 (1993), 205-210
DOI: https://doi.org/10.1090/S0002-9939-1993-1166353-0

Abstract:

It was proved by Choi that one can solve the Dirichlet problem at infinity for simply connected negatively curved manifolds by constructing appropriate convex sets. All the known constructions, it seems, inherently need some kind of growth condition on the curvature; therefore, it is interesting to find new ways to construct convex sets in negatively curved manifolds. In this paper we give a new way to construct convex sets from sets we call $\varepsilon$-almost-convex. From the point of view of this problem this can be considered as a natural generalization of convexity.
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 205-210
  • MSC: Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1166353-0
  • MathSciNet review: 1166353